Problem: Which of the following ordered pairs represents a solution to the equation below? $(-2, -7) (-1, -3) (0, -2) (1, -1) (2, 0)$ $y = 2x-2$
Solution: We can try plugging in the x-value of each ordered pair into the equation. If we evaluate and get the y-value of the ordered pair, then that ordered pair is a solution! Let's consider $(-2, -7)$ If we plug in $-2$ for $x$ and evaluate, do we get $-7$ $y = (2)(-2) - 2 = -4 - 2 = -6$ Let's consider $(-1, -3)$ If we plug in $-1$ for $x$ and evaluate, do we get $-3$ $y = (2)(-1) - 2 = -2 - 2 = -4$ Let's consider $(0, -2)$ If we plug in $0$ for $x$ and evaluate, do we get $-2$ $y = (2)(0) - 2 = 0 - 2 = -2$ Let's consider $(1, -1)$ If we plug in $1$ for $x$ and evaluate, do we get $-1$ $y = (2)(1) - 2 = 2 - 2 = 0$ Let's consider $(2, 0)$ If we plug in $2$ for $x$ and evaluate, do we get $0$ $y = (2)(2) - 2 = 4 - 2 = 2$ Thus the only ordered pair that is a solution to the equation is $(0, -2)$ We come to the same answer by plotting the points and the equation. $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$ $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$